In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

翻译：本文研究了高阶结构预测任务中的推断问题。在马可夫随机场中，高阶推断任务的目标是在标签空间上最大化一个得分函数，该得分函数可分解为单点势能和高阶势能之和。我们采用生成式模型方法来研究高阶推断问题，并提出一种用于精确标签恢复的两阶段凸优化算法。此外，我们建立了一类与超边扩张相关的超图结构性质，该性质驱动了一般高阶推断问题的成功求解。最后，我们利用一种新型超图Cheeger型不等式，将算法性能与超边扩张性质联系起来。